Integrated circuits for use at high frequencies often include high frequency interconnections such as coupled transmission lines, junctions, spirals, etc. Precise characterization of such high-frequency interconnections is very important for circuit simulation and optimization purposes.
Various numerical full-wave electro-magnetic (EM) analysis techniques have been used to characterize these interconnect structures. Solutions to the characterization problem based on solving, Maxwell's equations using the method of moments, finite elements, and finite difference time domain methods have all been utilized. While these numerical techniques are very accurate, they require large amounts of computer time. It might, for example, take days to optimize a simple microstrip stub filter consisting of only a handful of transmissions lines, tees and open ends. As a result, these techniques are not suitable for direct use in CAD software for simulation and optimization of integrated circuits containing such circuit elements.
One method for avoiding the high computer workload of EM simulations in the CAD software is to compute a model of a circuit element based on a large number of EM simulations. This model is then used to compute the relevant circuit parameters during the CAD simulation and optimization. In the simplest approach, look-up tables are used to access data computed by the EM analysis software representing a circuit element having various dimensions. This model is then utilized during, the CAD simulation. The circuit representation (scattering, parameters or transmission line parameters) of a circuit or sub-circuit is calculated prior to the CAD simulation on a fixed grid of samples in the parameter space (discrete width, height, angle, spacing . . . ) at some discrete frequencies, and the data is stored in a database. An approximate model is then computed during the CAD simulation by interpolation of the results stored in the database.
Using some form of simple curve fitting can augment the simple look-up table approach. In these systems, the dimension of the parameter space is often limited to 1. The commonly used fitting, functions include polynomials, rational functions and trigonometric functions.
Another prior art modeling technique uses Artificial Neural Networks (ANN's) to generate parameterized models. In these systems, a number of training and testing samples are randomly chosen in the parameter space and along the frequency axis, and an ANN is trained to model the circuit behavior.
The modeling techniques described above all have some important limitations. Look-up table systems without interpolation are limited to the set of precalculated structures. Such systems seldom have sufficient data to optimize a design.
Systems that utilize interpolation or curve fitting allow the designer to specify arbitrary model parameters within the boundaries of the model. However, the accuracy and efficiency of these techniques is often questionable. Some parts of the parameter and frequency space will, in general, be oversampled, while other parts are undersampled. Oversampling wastes computational resources, while undersampling leads to a poor correlation between the model and circuit performance. In addition, the disk space required for multidimensional table-based models can be quite high.
Interpolation systems and curve fitting systems cannot guarantee a predetermined level of accuracy. Furthermore, curve-fitting techniques often have artifacts. In addition, these techniques have difficulty modeling, the frequency behavior of resonant structures.
Techniques based on artificial neural networks can provide compact high-dimensional and highly non-linear models that overcome many of these problems. However, these techniques also have some serious drawbacks. There is no a priori method for defining a suitable net topology for an arbitrary circuit element. The number of hidden layers and nodes must be found by trial and error. In addition, frequency behavior is difficult to model. Once the user has decided on a particular ANN structure, there are long, training times. Finally, there is no easy method for determining, the accuracy of the resulting model.
Broadly, it is the object of the present invention to provide an improved method for generating, models for passive interconnect structures for use in circuit simulators.
It is a further object of the present invention to provide a method that automatically determines the data points and the number of degrees of freedom needed to model the structure with a predefined accuracy.
These and other objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention and the accompanying drawings.